How to have the texture of a circle separated in bands each with a different factor (or color) in a shader?
Since most earlier answers to this question, Blender has provided a discontinuous White Noise texture node. Even the smallest change in its 'coordinate' will produce a completely new output in the 0-1 range...

.. so your seed can simply be an addition to the 'W' input of the 1D version.

Here, keyed, but could be driven by #frame, location, or whatever is appropriate to your case.